Details

sample44.0ms

Algorithm

intervals

Results

12.0ms	201×	body	80	valid
6.0ms	256×	pre	80	true
4.0ms	14×	body	1280	valid
3.0ms	18×	body	320	valid
3.0ms	12×	body	640	valid
1.0ms	11×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2315
3	458
2	99
1	32
0	16

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
0.0b	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
12.9b	(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
16.3b	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`times-frac`
11×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/l*`
4×	`expm1-log1p-u` `fma-udef` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `swap-sqr` `associate-r` `associate-l*`
2×	`associate-/l/`
1×	`pow2` `distribute-rgt-in` `cbrt-undiv` `clear-num` `frac-2neg` `distribute-lft-in` `pow-plus` `flip3--` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `flip--` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

0.0ms	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
6.0ms	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
0.0ms	(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
12.0ms	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

series733.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
90.0ms	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
292.0ms	(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
214.0ms	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

simplify2.8s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
3	3884
2	1077
1	377
0	168

prune608.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ beta alpha) (fma i 2 (+ beta alpha)))
0.0b	(/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
0.1b	(* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))))
2.5b	(+ (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
68×	`times-frac`
42×	`add-cube-cbrt`
26×	`associate-r`
20×	`add-cbrt-cube` `add-exp-log`
18×	`distribute-lft-out`
16×	`associate-l`
9×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
7×	`associate-/r*`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv` `unswap-sqr` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `+-commutative` `sum-log` `fma-def` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 169

Calls

4 calls:

29.0ms	(/ (+ beta alpha) (fma i 2 (+ beta alpha)))
31.0ms	(/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
77.0ms	(* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))))
16.0ms	(+ (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

series868.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (+ beta alpha) (fma i 2 (+ beta alpha)))
142.0ms	(/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
366.0ms	(* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))))
277.0ms	(+ (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

simplify2.1s

Counts

181 → 181

Iterations

Iter	Nodes
done	5001
2	2441
1	717
0	242

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
0.1b	(/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha)))
1.3b	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha))))
3.4b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha)))) 1.0)

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

319×	`times-frac`
290×	`*-un-lft-identity`
215×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
82×	`associate-r`
42×	`distribute-lft-out`
33×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r/`
11×	`flip3-+` `flip-+`
10×	`div-inv`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/`
1×	`+-commutative` `sum-log` `fma-def` `flip3--` `pow-prod-down` `associate-r/` `-commutative` `flip--`

Counts

4 → 302

Calls

4 calls:

32.0ms	(/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
41.0ms	(/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha)))
40.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha))))
37.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha)))) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
221.0ms	(/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha)))
356.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha))))
289.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha)))) 1.0)

simplify2.9s

Counts

314 → 314

Iterations

Iter	Nodes
done	5001
2	3756
1	1079
0	386

prune1.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.3b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
0.2b	(exp (log (fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
2.5b	(fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
3.3b	(log (fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
20×	`times-frac`
18×	`add-cube-cbrt`
7×	`add-exp-log`
6×	`pow1` `log-prod` `add-cbrt-cube` `distribute-lft-out`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `exp-prod` `associate-/r*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum`
2×	`associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-sub` `div-exp` `rem-log-exp` `flip-+` `fma-udef` `div-inv` `flip--` `rem-exp-log`

Counts

4 → 93

Calls

4 calls:

16.0ms	(/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
3.0ms	(exp (log (fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
0.0ms	(fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
3.0ms	(log (fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))

series893.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
208.0ms	(exp (log (fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
197.0ms	(fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
366.0ms	(log (fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))

simplify2.5s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
3	4343
2	966
1	358
0	162

prune586.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.3b

regimes468.0ms

Accuracy

0% (0.3b remaining)

Error of 12.1b against oracle of 11.9b and baseline of 12.1b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample2.4s

Algorithm

intervals

Results

774.0ms	6380×	body	80	valid
743.0ms	8000×	pre	80	true
303.0ms	500×	body	1280	valid
240.0ms	538×	body	640	valid
93.0ms	362×	body	320	valid
40.0ms	220×	body	160	valid